(imported comment written by Lee Wei)
Here is one idea that might work for you.
While you cannot extract the data easily from an existing Web Report, you can probably embedded the entire Web Reports page in a iFrame.
Find the Report ID of your custom report, then construct a URL to include the some generic reporting credential.
For example, when I run a report, I see this URL:
I change it to the following and it should work to directly access your report.
http://tintin:52312/webreports?page=CustomReport&ReportID=20&Username=leewei&Password=welcome
You can include the Username and Password in a form post rather than URL to make it less visible. Obviously the credentials are exposed, so you will have to decide if the convenience is appropriate and security exposure feasible.
Lee Wei